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Fault-tolerant computation
• computing requires isolation & control • maybe no such qubits occur "naturally" • fault-tolerance: generic approach • noise has to be weak & weakly correlated
in spacetime • here: arbitrary correlations in time
Quantum memories based on single-shot error correction
exhibit an error threshold under spatially local stochastic noise
syndrome extraction
Error correction
logical qubit physical qubits
extra d.o.f. check ops
correctiondecoding
Error correction
syndrome extraction
correctiondecoding
local, quantum global, classical local, quantum
single-shot if quantum-local
(analogous to LOCC)
Quantum memory
Perfect encoding and decoding to test the quality of the quantum memory:
alternated noise and noisy error correction
For error rates below a threshold
where a & b decrease exponentially with the system size.
Quantum memory
• Universal computation probably straightforward • D < 3 • Known fabrication faults • Fully local (CA) error correction • The physics of gauge color codes. Gapless
phases? Confinement?
DISCUSSION